1. Field of the Invention
This invention relates to tools for computer modeling and information system tools for the study of the dynamic behavior—natural, desirable, undesirable, etc.—of wide ranges of chemical and biochemical reaction networks, such as signaling cascades, having nonlinear mathematical models (for example involving products of state variables and models of allosteric enzymes) and, particularly, to the creation of structured catalogs of known and hypothetical chemical reaction networks (including structured mathematical models), the creation of mathematical modeling tools targeted at uncovering ‘hidden’ behaviors suspected of said nonlinear mathematical models, and the use and interworking of these individually or in combination with one another and other external information, modeling, analysis, interactive, and presentation systems and methods.
The system and method herein can be applied to a wide range of life science applications, including disease research, metabolic research, and drug design as well as applications in nanotechnology, sensors, chemical computation, and chemical plant operation.
2. Background and Related Art
Over the last few decades there has been considerable increase in interest in signaling and signal transduction networks within biological systems. Study of these has yielded tremendous value in the understanding of disease, metabolism, drug discovering, DNA transcription, and a number of other areas. Future study appears to hold rich promise, as these basic frameworks of biochemical communication are involved in almost all aspects of life processes. Additionally, these biochemical communications channels—together with their implicit controlling and regulatory structures—can be adapted to great value in future nanotechnology systems, manufacturing, and other non-life-science applications.
Implicit in biological signaling and signal transduction are individual sequences of chemical reactions. Each of these sequences begins with a chemical reaction of one kind, which, as it progresses, subsequently initiates one or more chemical reactions of another kind. The latter reaction in turn would cause one or more additional types of subsequent reactions to occur, and so on, to form chain that can act as a chemical channel for carrying information. The typical links in the chain are the products produced in a given chemical reaction being such that they initiate the reaction that follows it. Because the information is carried by a stimulus being transformed by each reaction in the chain, the term “transduction” is applied, in analogy with transducers that transform an input optical, mechanical, electrical, or mechanical stimulus into an output stimulus of another type. Signaling occurs within cells, within substructures of cells, among cells, and can also occur organism-wide.
In naturally occurring biological systems, there are significant numbers of wide-ranging types of signaling and signal transduction communications channels. The coexistence and structured interactions of these form a network, hence the notion of signaling and signal transduction networks. A startling 20% (that is ⅕) of the coding genes in humans encode for proteins directly involved in signal transduction [Venter01]. Signaling and signaling pathology also occurs in plants and animals.
The constituent biochemical signaling and signal transductions in the environments where they occur are extraordinarily dependable, implementing or supporting almost every life process on the planet. However, biochemical signal transductions can sometimes go awry. Such signal transductions process failure has been explicitly linked to decease, illness, and pathology, including cancer. For example, dysregulation of the Signal Transducer and Activator of Transcription (“Stat”) proteins, RAF kinase signaling pathways (such as Ras/RAF/MEK/ERK), cell cycle Cyclin-CDK complexes aspects of mitosis-promoting factors, growth factor roles in chemical signaling pathways, and many other signaling pathways have been implicated in cancer. A few of the many know or conjectured other examples of signaling pathways involved in disease can be found in the books [CarBri07], [BrCaMZ04], [Frank03], [Boyd91] and a host of articles publishing monthly worldwide.
These failures can result from variations in the ambient reaction environment or from unintended “cross talk” (coupling) between individual reactions in two or more biochemical signal transduction pathways (or even within the same pathway). Modes of failure and their behavior can be widely variant and remain poorly understood. It is to this, and a number of related problems and applications, that the present invention is directed.
More specifically, despite the extensive study of biochemical signal transductions the area remains poorly understood. Much effort and success has been made in identifying specific sequences of chemical reactions in specific metabolic and transcriptional pathways and the constituents of these. However, the internal structure of the specific reaction types are less understood and few dynamic behaviors have been reduced to representative mathematical models. Additionally, few of the reaction constants, which determine the dynamic behavior of the mathematical models, have been viably measured in ways relevant to their in situ occurrences.
Further, even for known mathematical models, the dynamics quite often comprise nonlinear differential equations. Few researchers can work well with these, and so often these nonlinear differential equations are linearized (removing their nonlinear character) and/or studied in steady-state equilibrium (setting all time derivatives to zero) therefore miss both the intrinsic nonlinearities and intrinsic dynamics. In other fields of study (such as electronic communications and dynamic control systems) involving nonlinear differential equations, it is through the detailed study of the nonlinear dynamics behavior that reveals essential aspects of instability, trajectory bifurcations, sensitivity to outside disturbances at specific points in the signal chain, and other key aspects relatively to questions of robustness and failure modes. It is additionally to this, and a number of other related problems and applications, that the present invention is directed.
Additionally, computer models exist for the numerical simulation of the dynamics of classical enzyme reactions. Most of these are directed to the kinetics of isolated enzyme reactions, although a few are directed towards enzyme cascades in particular. Although useful, these computer models do not provide structural stability analysis of the larger nonlinear enzyme cascade dynamics (as may be valuable for revealing essential aspects of instability, trajectory bifurcations, sensitivity to outside disturbances at specific points in the signal chain, and other key aspects relating to questions of robustness and failure modes).
Turing from reaction modeling specifically, attention is directed to the immensely active area of bioinformatics systems.
Bioinformatics systems are well known and have evolved from conventional database technologies to broader types of systems incorporating chemistry computations involve that involve knowledge representation, knowledge processing, symbolic computation, expert systems, predicate logic reasoning, machine learning, evolutional computation, and neural network computation (see, e.g., [Schulze95]). These have a traditional orientation towards molecular structure, molecular topology, molecular typography, molecular classification schemes, amino acid sequencing, conformation and folding properties, chemical properties, receptor site characterization, and aspects of reaction graphs. Also there are a number of tools for modeling differential equations and chemical reactions.
Even as the field of bioinformatics is exploding, so is the expanding identification of metabolic signal transduction mechanisms involving enzyme cascades and other types of chemical reaction networks (for example, involving free metal ions such as calcium, sodium, and potassium, ions of chlorine, etc.). A large number of signaling transduction networks are known, most albeit in early identification, and are typically barely understood in isolation and even less understood in their broader intertwine operations and roles within the organism. Some of the complications include:                The poor understanding and characterization of the types of differential equations that naturally model most signal transduction processes, for example such as enzyme cascades. In particular, many signaling cascades involving catalytic multiplying effects which model as a multiplicative product between the concentration of two or more chemical species within or in ambience of the cascade. These equations are typically correctly identified, but then linearized, studied in equilibrium conditions (by setting all time derivatives equal to zero), partial equilibrium (setting fast-reaction derivatives equal to zero), or at best studied with numerically computed solutions in idealized, simplified settings.        The extensive opportunities for explicit “crosstalk” among signal transduction pathways, where one signaling transduction path's chemistry affects another signal transduction path, as well as situations where exogenous processes affect the ambient environment of the signal transduction path. The former of these, explicit crosstalk, is controversial as there are many more opportunities for it (analogies have been made to sloppy software “spaghetti code” resulting from eons of incremental chemical evolution) yet many arguments can be made as to signaling paths being so localized (for example, as is well appreciated in calcium signaling) that there is limited natural opportunity in living organisms for such signal transduction pathway crosstalk interference.        
The limited understanding in both of these areas has further compounding concerns, for example:                The types of differential equations involved can be modeled as types of so-called ‘bilinear control systems’ which have had some study in the context of both engineering (electrical, chemical, and nuclear) and in abstract mathematics (involving Lie algebras of matrices). In even the limited understanding of those systems, a wide range of hidden and unexpected properties are possible, including several surprising modalities that lead to instabilities and wide deviation form quiescent behavior [Ludwig80], [Mohler73], some examples of which will be provided later.        Other types of nonlinear behavior, for example hysteresis, chemical chaos, chemical self-organization, etc. can emerge in these systems under certain quantifiable conditions.        Even if crosstalk and where situation where exogenous processes affect the ambient environment of the signal transduction path are relatively rare, the fact that a daily increasing number of metabolic problems and pathologies as well as drug design and analysis isolate variation and interference with signal transduction pathways make expanded understanding of this area still potentially quite valuable.        
What would therefore appear to be an extremely valuable and useful tool in current and future metabolic and drug research for humans and animals, study and treatments of plant pathologies, design of chemical sensors and nanotechnologies, as well as potentially creating valuable new research directions, are systems and methods combining the following:                A structured catalog of signal transduction pathways, each including:                    structural mathematical models of the reaction dynamics;            values of coefficients and parameters of these models;            known related chemistry of the pathway's chemical constituents;                        Mathematical tools for checking the structural behavior of these mathematical models, in particular designed to be operative for:                    Identification of internal proclivities towards instabilities;            Identification of potential sensitivities to known and unknown candidate crosstalk processes;            Identification of potential sensitivities to ambient chemical environments;                        Ability to combine isolated models into a larger model which in turn can be checked in the manner above as the combined models (for example, those which crosstalk with one another) as the combined models will likely behave differently than the isolated models;        Ability to replace models or groups of models with other models or groups of models for various reason, such as but not limited to:                    Incorporation of improved models;            Incorporation of more comprehensive models;            Incorporation of simplified models;            Incorporation of more isolated models;            Incorporation of trial hypothetical models;            Incorporation of perturbation(s) and/or control(s) into models;            Naturally support evolution of models;            Study of legacy models;                        Provide a standardized framework, I/O handling, and variable handling for models for various reason, such as but not limited to:                    Exchange of models among groups of researchers;            Provide for sale, licensing, and/or purchase of models.                        
In addition, the arrangement described above can be recast to address a broader range of chemical reaction networks, including non-biological ones, which to date have had limited development and tools [RodRod64], [TeZeBo96]. Such a recast arrangement could be particularly valuable in traditional technologies such as the design of controlled chemical reaction sequences in chemical plants, the design and operation of chemical plants themselves, and failure analysis of controlled chemical reaction sequences and chemical plants. Further, such a recast arrangement can facilitate new chemical-based information processing technologies that can be incorporated into or create entirely new types of chemical sensors and nanotechnology devices.
Further, as nanoscale technologies and other technology advances unite chemical reaction networks, supramolecular chemistry, conventional electronics, molecular electronics, optical-electronic processes, optical-chemical processes, small-scale mechanics, molecular computing, quantum computing, and other phenomenon, the invention can be expanded into a Computer-Aided Design (“CAD”) tool for integrated multi-process dynamical design. This is a straightforward expansion of the invention as all that is required is an expansion of the type and number of mathematic models, catalog entries, and catalog fields.